Modeling the effects of small turbulent scales on the drag force for particles below and above the Kolmogorov scale

Consistently with observations from recent experiments and DNS, we focus on the effects of strong velocity increments at small spatial scales for the simulation of the drag force on particles in high Reynolds number flows. In this paper, we decompose the instantaneous particle acceleration in its systematic and residual parts. The first part is given by the steady-drag force obtained from the large-scale energy-containing motions, explicitly resolved by the simulation, while the second denotes the random contribution due to small unresolved turbulent scales. This is in contrast with standard drag models in which the turbulent microstructures advected by the large-scale eddies are deemed to be filtered by the particle inertia. In our paper, the residual term is introduced as the particle acceleration conditionally averaged on the instantaneous dissipation rate along the particle path. The latter is modeled from a log-normal stochastic process with locally defined parameters obtained from the resolved field. The residual term is supplemented by an orientation model which is given by a random walk on the unit sphere. We propose specific models for particles with diameter smaller and larger size than the Kolmogorov scale. In the case of the small particles, the model is assessed by comparison with direct numerical simulation (DNS). Results showed that by introducing this modeling, the particle acceleration statistics from DNS is predicted fairly well, in contrast with the standard LES approach. For the particles bigger than the Kolmogorov scale, we propose a fluctuating particle response time, based on an eddy viscosity estimated at the particle scale. This model gives stretched tails of the particle acceleration distribution and dependence of its variance consistent with experiments

Assessment of LES-STRIP approach for modeling of droplet dispersion in diesel-like sprays

International audienceIn this paper, the stochastic equations of droplet motion in turbulent flow, proposed recently by Gorokhovski and Zamansky (2018, Phys. Rev. Fluids 3, 3, 034602), are assessed for turbulent spray dispersion in diesel like conditions along with Large Eddy Simulation (LES) for the gaseous flow. For droplets above the Kolmogorov length scale, this model introduces the concept of the stochastic drag, independently of laminar viscosity. For droplets below the Kolmogorov length scale, the model equation does depend on the laminar viscosity through the Stokes drag but the particle motion is stochastically forced. Both the stochastic drag and the stochastic forcing of the Stokes drag equation are based on the simple log-normal stochastic process for the viscous dissipation (ϵ) “seen” along the droplet trajectory. In this paper, this model is applied in the framework of two-way coupling, wherein the turbulence generated by the spray inturn controls the spray dispersion. The criterion for the choice of one of the approaches, i.e., the stochastic drag or the stochastic forcing, follows the classical condition for drag coefficient based on the droplet Reynolds number (Re p). The non-vaporizing spray experiments from Engine Combustion Network (ECN) are used as test cases. In addition to the comparison of the spray penetration length, spreading angle and spray structure with the experimental data, a qualitative analysis of the statistics of the droplet acceleration and gas phase velocities is presented. It was shown that the new approach is much more effective in modeling the spray dynamics on relatively coarser mesh. Consequently, the new approach in the framework of two-way coupling may predict the preferential concentration effects better, which is important for spray combustion

Modèle de turbulence développée basé sur la théorie du groupe et renormalisation des équations de Navier-Stokes

Dans ce travail nous avons essayé de décrire mathématiquement la turbulence stationnaire homogène à partir des équations de Navier-Stokes, en s'affranchissant des hypothèses classiques basées sur l'intuition. En particulier, nous avons utilisé les propriétés de symétrie de l'équation d'Euler. La démarche consistait à associer l'état turbulent stationnaire aux solutions spécifiques auto-similaires périodiques de l'équation d'Euler soumises aux symétries fondamentales de translation, de rotation et d'échelle. Pour un tel champ turbulent, il s'ensuit un résultat significatif : dans le cas homogène, la composition des transformations, liées aux symétries de translation, de rotation et d'échelle, équivaut à passer d'une épaisseur du filtrage de vitesse à une autre, plus grande. Cette propriété de passage « du micro à macro » a été appelée l'invariance de groupe de renormalisation. Elle a permit d'obtenir une forme renormalisée des équations de Navier-Stokes. Ici, la viscosité turbulente apparaît à partir de la viscosité laminaire et non suite aux contraintes de type Reynolds exprimées habituellement en fonction des gradients de vitesse moyens à l'aide de l'hypothèse de Boussinesq

Further development of Level Set method (modified level set equation and its numerical assessment)

Pas de résuméThe level set method was introduced by Osher & Sethian (1988) as a general technique to capture moving interfaces. It has been used to study crystal growth, to simulate water and fire for computer graphics applications, to study two-phase flows and in many other fields. The wellknown problem of the level set method is the following: if the flow velocity is not constant, the level set scalar may become strongly distorted. Thus, the numerical integration may suffer from loss of accuracy. In level set methods, this problem is remedied by the reinitialization procedure, i.e. by reconstruction of the level set function in a way to satisfy the eikonal equation. We propose an alternative approach. We modify directly the level set equation by embedding a source term. The exact expression of this term is such that the eikonal equation is automatically satisfied. Furthermore on the interface, this term is equal to zero. In the meantime, the advantage of our approach is this: the exact expression of the source term allows for the possibility of derivation of its local approximate forms, of first-and-higher order accuracy. Compared to the extension velocity method, this may open the simplifications in realization of level set methods. Compared to the standard approach with the reinitialization procedure, this may give the economies in the number of level set re-initializations, and also, due to reduced number of reinitializations, one may expect an improvement in resolution of zero-set level. Hence, the objective of the present dissertation is to describe and to assess this approach in different test cases.LYON-Ecole Centrale (690812301) / SudocSudocFranceF

Modélisation stochastique de l'atomisation primaire et secondaire couplée à la LES

Ce travail présente un modèle d'atomisation primaire assistée par gaz dans un spray turbulent à fort nombre de Weber. L'atomisation primaire est simulée de façon stochastique : la diminution de l'épaisseur du coeur liquide dans la direction transverse à l'écoulement est gouvernée par la fragmentation avec hypothèse de symétrie d'échelle. A partir des statistiques du cœur liquide au voisinage de l'injecteur, des gouttes sont formées en utilisant une distribution présumée et en respectant la conservation de la masse. Les gouttes sont soumises à l'atomisation secondaire et à la coalescence. Ces phénomènes sont simulés de façon stochastique comme résultant des collisions entre gouttelettes. La modélisation du spray est couplée à la simulation des grandes échelles pour la phase gazeuse. Les résultats de calculs sont comparés aux travaux expérimentaux : pour la distribution de présence de liquide au voisinage de l'injecteur ; et loin de l'injecteur, pour le diamètre de Sauter moyen

RANS and LES of multi-hole sprays for the mixture formation in piston engines

Cette thèse porte sur la simulation des jets de gouttes générés par des pulvérisateurs essence haute pression, pulvérisateurs qui sont un point clef des systèmes de combustion automobile de la présente et future génération devant diminuer les émissions de CO2 et de polluants. Dans un premier temps les jets de gouttes ( sprays ) sont simulés par simulation moyennée. Les résultats de simulation d un jet donnant des résultats en moyenne satisfaisant, l'interaction de jets en injecteurs multi-trous est alors simulée. Les résultats sont cohérents par rapport aux mesures d'entraînement d air. La simulation permettant d'avoir accès au champ complet 3D, le mécanisme d'interaction jet à jet et de développement instationnaire du spray est décrit en détail. La formation d un mouvement descendant au centre du spray et celle d'un point d'arrêt central sont trouvés. Finalement, Ces résultats sont étendus au cas surchauffé, cas où la pression dans la chambre est inférieure à la pression de vapeur saturante. Un modèle simple semi-empirique est proposé pour tenir compte de la modification des conditions proches de la buse d injection. Le modèle prédit correctement les tendances des variations de paramètres et capture la forme générale du spray qui se referme sur lui-même. La seconde grande partie est consacrée au développement d un modèle de spray par l approche des grandes échelles (SGE), limité ici aux cas non évaporant. Il comprend la modélisation de sous-maille de la dispersion turbulente, des collisions-coalescence et des termes d échange de quantité de mouvement de sous-maille. L'effet du choix du modèle de sous-maille pour la viscosité turbulente de sous-maille est montré, le choix retenu étant le modèle de Smagorinski dynamique. Afin d'améliorer la représentativité cruciale des conditions d injections, un couplage faible est réalisé à partir de résultats de simulations existantes de l'écoulement interne aux buses. Les fonctions densité de probabilité simple et jointes extraits des résultats de simulations sont validés par rapport aux mesures PDA en situation pseudo-stationnaire et la pénétration liquide et la forme du spray est comparée aux visualisations par ombroscopie. Enfin, différentes zones caractéristiques sont identifiées et des longueurs sont notées pour les cas d'injection à 100 et 200bar.Over the years numerical modelling and simulation techniques have constantly been improved with the increase in their use. While keeping the computational resources in mind, numerical simulations are usually adapted to the required degree of accuracy and quality of results. The conventional Reynolds Average Navier Stokes (RANS) is a robust, cheap but less accurate approach. Large Eddy Simulation (LES) provides very detailed and accurate results to the some of the most complex turbulence cases but at higher computational cost. On the other hand, Direct Numerical Simulation (DNS) is although the most accurate of the three approaches but at the same time it is computationally very expensive which makes it very difficult to be applied to the most of the complex industrial problems. The current work is aimed to develop a deeper understanding of multi-hole Gasoline Direct Injection (GDI) sprays which pose many complexities such as; air entrainment in the multi-hole spray cone, Jet-to-Jet interactions, and changes in the spray dynamics due to the internal flow of the injector. RANS approach is used to study multi-hole injector under cold, hot and superheated conditions. Whereas, LES is utilized to investigate the changes in the dynamics of the single spray plume due to the internal flow of the GDI injector. To reduce computational cost of the simulations, dynamic mesh refinement has been incorporated for both LES and RANS simulation. A thorough investigation of air entrainment in three and six hole GDI injectors has been carried out using RANS approach under non superheated and superheated conditions. The inter plume interactions caused by the air entrainment effects have been analysed and compared to the experimental results. Moreover, the tendencies of semi collapse and full collapse of multi-hole sprays under non superheated and superheated conditions have been investigated in detail as well. A methodology of LES has been established using different injection strategies along with various subgrid scale models for a single spray plume. In GDI multi-hole sprays, the internal flow of the injector plays a very crucial role in the outcome the spray plume. A separate already available internal flow LES simulation of the injector has been coupled with the external spray simulation in order to include the effect of nozzle geometry and the cavitation phenomenon which completely change the dynamics of the spray.LYON-Ecole Centrale (690812301) / SudocSudocFranceF

Air Entrainment in High Pressure Multihole Gasoline Direct Injection Sprays

Experimental and numerical investigation of multihole gasoline direct injection (GDI) sprays at high injection pressure and temperature are performed. The primary objective of this study is to analyse the role of gas entrainment and spray plume interactions on the global spray parameters like spray tip penetration, spray angles and atomization. Three-hole 90° spray cone angle and six-hole 60° spray cone angle injectors are used for current work to examine the effect of the geometry of the injector on the spray interactions. The numerical results from Reynolds Average Navier Stokes (RANS) simulations show a reasonable comparison to experiments. The simulations provide further insight to the gas entrainment process highlights the fact that a stagnation plane is formed inside the spray cone which basically governs the semi collapse of spray that in turn affects the spray direction and cone angle